References

[1] Pankaj Agarwal, Lars Arge and Andrew Danner. From Point Cloud to Grid DEM: A Scalable Approach. In Proc. 12th Intl. Symp. on Spatial Data Handling (SDH), 2007

[2] Lars Arge, Henrik Blunck and Anders Hesselund-Jensen, "I/O-efficient Quadtree Construction and Leaf Neighbor Finding“, draft.

[3] Lars Arge, Henrik Blunck and Anders Hesselund-Jensen, "I/O-efficient Nearest Neighbor Algorithms for Grid DEM Quality Evaluation, draft.

Grid DEM quality metrics Problem: Often grid DEM points are interpolated from very distant input

points. User would like to know “trustworthiness” of each grid point

Contour line visualization of a grid. There are obvious flaws in the vicinity of buildings (where no input points are available)

Our approach: We compute nearest input point for each grid DEM cell

I/O-efficient algorithm: We compute nearest points by adapting known nearest-neighbor algorithms and exploiting uniformity of grid [3]

Visualizations of our measure. Areas with very close input points are green, areas with relatively close input points are blue and areas with

distant input points are red

Integration into TerraSTREAMDigital elevation models (DEM)

Digital Elevation Model (DEM) is a representation of a terrain

Two main DEM models

Uniform grid (Grid)

Triangulated irregular network (TIN)

A DEM is usually constructed from a finite set of height measurements (e.g., LAS LIDAR data)

Grid DEMs and their construction Grid DEM is a uniform grid of height values

Advantage: Simple terrain analysis algorithms

Drawbacks / Challenges:

Inefficient representation of highly varying terrain

Need to interpolate input data points when constructing grid DEM

Adaptive construction:

We adaptively break grid into tiles containing “few” input data points

We interpolate in each tile independently, also considering data points in neighbor tiles (to ensure smoothness along boundaries)

MADALGO – Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation

TerraSTREAM: Grid DEM Construction and Quality Metric

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Height grid3D visualization of a height grid

Tiling of a point data set A tile to interpolate and its neighbors

Observation: One can compute tiling I/O-efficiently to be able to process massive amount of input data [1,2]

Improved algorithm: Cache-oblivious processing of z-ordered tiles in a single main pass [2]:

Presort points according to their order along Z-curve so to resemble on disk the spatial locality of input

Scan through z-ordered points, constructing tiles “on the fly”.

During scan: For interpolation in each tile its neighbors can be accessed efficiently using a cache-oblivious priority queue

Points in Quadtree ordered along Z-curve

Neighbors of a quadtree cell

Grid DEM quality metric

Grid DEMs and construction basics

Digital Elevation Models (DEMs) I/O-efficient adaptive Grid DEM construction

References

Grid/TIN Construction

Flood Simulation

Topological Simplification

Flow Routing

Flow Accumulation

Pfafstetter Labeling

Contour Map Generation

Grid Quality Metric